hh_cond_beta_gap_traub – Hodgkin-Huxley neuron with gap junction support and beta function synaptic conductances
================================================================================================================

Description
+++++++++++

``hh_cond_beta_gap_traub`` is an implementation of a modified Hodgkin-Huxley model
that also supports gap junctions.

This model was specifically developed for a major review of simulators [1]_,
based on a model of hippocampal pyramidal cells by Traub and Miles [2]_.
The key differences between the current model and the model in [2]_ are:

- This model is a point neuron, not a compartmental model.
- This model includes only ``I_Na`` and ``I_K``, with simpler ``I_K`` dynamics than
  in [2]_, so it has only three instead of eight gating variables;
  in particular, all Ca dynamics have been removed.
- Incoming spikes induce an instantaneous conductance change followed by
  exponential decay instead of activation over time.

This model is primarily provided as reference implementation for hh_coba
example of the Brette et al (2007) review. Default parameter values are chosen
to match those used with NEST 1.9.10 when preparing data for [1]_. Code for all
simulators covered is available from ModelDB [3]_.

Note:
In this model, a spike is emitted if :math:`V_m \geq V_T + 30` mV and
:math:`V_m` has fallen during the current time step.

To avoid that this leads to multiple spikes during the falling flank of a
spike, it is essential to chose a sufficiently long refractory period.
Traub and Miles used :math:`t_{ref} = 3` ms ([2]_, p 118), while we used
:math:`t_{ref} = 2` ms in [2]_.

Postsynaptic currents
Incoming spike events induce a postsynaptic change of conductance modelled by a
beta function as outlined in [4]_ [5]_. The beta function is normalized such that an
event of weight 1.0 results in a peak current of 1 nS at :math:`t = \tau_{rise,xx}`
where xx is ex or in.

Spike Detection
Spike detection is done by a combined threshold-and-local-maximum search: if
there is a local maximum above a certain threshold of the membrane potential,
it is considered a spike.

Gap Junctions
Gap Junctions are implemented by a gap current of the form
:math:`g_{ij}( V_i - V_j)`.

Parameters
++++++++++

The following parameters can be set in the status dictionary.

============ ======  =======================================================
V_m          mV      Membrane potential
V_T          mV      Voltage offset that controls dynamics. For default
                     parameters, V_T = -63mV results in a threshold around
                     -50mV
E_L          mV      Leak reversal potential
C_m          pF      Capacity of the membrane
g_L          nS      Leak conductance
tau_rise_ex  ms      Excitatory synaptic beta function rise time
tau_decay_ex ms      Excitatory synaptic beta function decay time
tau_rise_in  ms      Inhibitory synaptic beta function rise time
tau_decay_in ms      Inhibitory synaptic beta function decay time
t_ref        ms      Duration of refractory period (see Note)
E_ex         mV      Excitatory synaptic reversal potential
E_in         mV      Inhibitory synaptic reversal potential
E_Na         mV      Sodium reversal potential
g_Na         nS      Sodium peak conductance
E_K          mV      Potassium reversal potential
g_K          nS      Potassium peak conductance
I_e          pA      External input current
============ ======  =======================================================

References
++++++++++

.. [1] Brette R et al (2007). Simulation of networks of spiking neurons: A
       review of tools and strategies. Journal of Computational Neuroscience
       23:349-98. DOI: https://doi.org/10.1007/s10827-007-0038-6
.. [2] Traub RD and Miles R (1991). Neuronal Networks of the Hippocampus.
       Cambridge University Press, Cambridge UK.
.. [3] http://modeldb.yale.edu/83319
.. [4] Rotter S and Diesmann M (1999). Exact digital simulation of
       time-invariant linear systems with applications to neuronal modeling.
       Biological Cybernetics 81:381 DOI: https://doi.org/10.1007/s004220050570
.. [5] Roth A and van Rossum M (2010). Chapter 6: Modeling synapses.
       in De Schutter, Computational Modeling Methods for Neuroscientists,
       MIT Press.

Sends
+++++

SpikeEvent

Receives
++++++++

SpikeEvent, CurrentEvent, DataLoggingRequest

See also
++++++++
:doc:`Neuron <index_neuron>`, :doc:`Hodgkin-Huxley <index_Hodgkin-Huxley>`, :doc:`Conductance-Based <index_conductance-based>`